{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression with Fixed Basis Functions and the IRLS Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import multivariate_normal, seed\n",
    "from branca.colormap import LinearColormap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(1643)\n",
    "\n",
    "S1 = np.array([\n",
    "    [.05, 0],\n",
    "    [0, 0.05]\n",
    "])\n",
    "\n",
    "\n",
    "S2 = np.array([\n",
    "    [.05, 0],\n",
    "    [0, .07]\n",
    "])\n",
    "\n",
    "\n",
    "x1 = multivariate_normal([0, 0], S1, 50)\n",
    "\n",
    "x2_1 = multivariate_normal([-1.5, -1.5], S2, 50)\n",
    "x2_2 = multivariate_normal([1.5, 1.5], S2, 50)\n",
    "x2 = np.r_[x2_1, x2_2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def phi(x, m, s):\n",
    "    return np.exp(-(x - m) ** 2 / s)\n",
    "\n",
    "phi2 = np.c_[phi(x2[:, 0], 0, 1.4), phi(x2[:, 1], 1, 1.2)]\n",
    "phi1 = np.c_[phi(x1[:, 0], 0, 1.4), phi(x1[:, 1], 1, 1.2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 936x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 781
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(13, 4))\n",
    "ax[0].scatter(*x1.T, s=10, c=\"tab:gray\")\n",
    "ax[0].scatter(*x2.T, c=\"tab:red\", s=10)\n",
    "ax[0].set_xlabel(\"$x_1$\", fontsize=15)\n",
    "ax[0].set_ylabel(\"$x_2$\", fontsize=15)\n",
    "\n",
    "ax[1].scatter(*phi1.T, c=\"tab:gray\", s=10)\n",
    "ax[1].scatter(*phi2.T, c=\"tab:red\", s=10)\n",
    "ax[1].set_xlabel(\"$\\phi_1$\", fontsize=15)\n",
    "ax[1].set_ylabel(\"$\\phi_2$\", fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cross-entropy loss for a two class problem is defined as the negative log-likelihood function of a Bernoulli random variable, where the probability is defined in terms of a weight vector $\\bf w$ and an input vector $\\bf x$:\n",
    "\n",
    "$$\n",
    "    E({\\bf w}) = - \\sum_{n=1}^N t_n \\log\\left(\\sigma({\\bf w}^T{\\bf x})\\right) + (1 - t_n) \\log\\left(1 - \n",
    "    \\sigma({\\bf w}^T{\\bf x})\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An approximation to the sigmoid function given by the probit functio\n",
    "\n",
    "The sigmoid function is given by\n",
    "$$\n",
    "   \\sigma(z) = \\frac{1}{1 + e^{-z}} \n",
    "$$\n",
    "\n",
    "on the other hand, the probit function is defined as\n",
    "$$\n",
    "    \\Phi(z) = \\int_{-\\infty}^z \\mathcal{N}(x | 0, 1) dx,\n",
    "$$\n",
    "\n",
    "Where $\\Phi(z)$ can be evaluated considering the error function\n",
    "$$\n",
    "    \\text{erf}(z) = \\frac{2}{\\sqrt\\pi} \\int_0^z e^{-\\theta^2 / 2} d\\theta\n",
    "$$\n",
    "\n",
    "via the relationship\n",
    "\n",
    "$$\n",
    "    \\Phi(a) = \\frac{1}{2}\\left(1 + \\frac{1}{\\sqrt{2}}\\text{erf}(a)\\right)\n",
    "$$\n",
    "\n",
    "\n",
    "#### Note\n",
    "An alternative definition of the error function defined inside the `scipy` liberary is given by $\\text{erf}(z) = \\frac{2}{\\sqrt\\pi} \\int_0^z e^{-\\theta^2} d\\theta$, in which case the CDF for a standard Gaussian distribution is given by $\\Phi(a) = \\frac{1}{2}\\left(1 + \\text{erf}\\left(\\frac{z}{\\sqrt{2}}\\right)\\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import erf\n",
    "\n",
    "def sigmoid(z): return 1 / (1 + np.exp(-z))\n",
    "def Phi(z): return (1 + erf(z / np.sqrt(2))) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xrange = np.linspace(-4, 4)\n",
    "plt.plot(xrange, sigmoid(xrange), label=\"sigmoid\")\n",
    "plt.plot(xrange, Phi(xrange), label=\"probit\")\n",
    "plt.legend()\n",
    "plt.grid(alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To approximate $\\sigma$, we consider a scaled version of the probit function $\\Phi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "cm = LinearColormap([\"blue\", \"teal\"], vmin=0.1, vmax=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x81a818940>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambdas = [0.1, 0.3, 0.5]\n",
    "for l in lambdas:\n",
    "    plt.plot(xrange, Phi(xrange * l), c=cm(l), label=r\"$\\lambda = {}$\".format(l), alpha=0.5)\n",
    "plt.plot(xrange, sigmoid(xrange), label=\"sigmoid\", c=\"crimson\")\n",
    "plt.grid(alpha=0.3)\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
